Sounds like the timing is not advanced enough. I recently adapted a DA single ignition to an RCS180. The timing was too retarded and it would sit there and just barely run over until somehow it would get enough rpm to trigger the DA ignitions advance curve, then it would take off and run great. I finally got the timing set about right and it ran fine after that. On a couple of occasions at half throttle it was still at idle rpm, and a few times it would just slow down and die, similar to what you are experiencing.

It could also be trash in the carburetor, but this would tend to make the engine just sag and instantly die when the throttle was opened, NOT continue running then catching itself, or slowly slowing down till it stopped.

I'd advise calling Keith at BME for a final analysis.